PDE Seminar

Stability of traveling waves of three dimensional Gross-Pitaevskii equation

王征平 教授 (武汉理工大学)

2017年4月14日10:00-11:00 闵行校区行政楼12楼PDE中心1202报告厅

Abstract. We present some recent results on the stability of traveling waves of three dimensional Gross-Pitaevskii (GP)equation. The GP equation is a nonlinear Schrodinger equation with nonzero condition at infinity, which has traveling waves with non-vanishing limit at infinity, first discovered by physicists (Jones, Roberts et al.) in 1980s. The existence of such traveling waves has been studied a lot in recent years by Betheul, Saut, Maris and many others. However, the stability and dynamical behaviors of these traveling waves are not well understood. In collaboration with Zhiwu Lin and Chongchun Zeng, we proved a nonlinear stability criterion for 3D traveling waves of GP equation as conjectured in the physical literature.